Question Number 225610 by Lara2440 last updated on 06/Nov/25 $$\mathrm{prove} \\ $$$$\mathrm{Gauss}\:\mathrm{curvature}\:{K}\:\mathrm{is}\:\mathrm{intrinsic}\:\mathrm{by}\:\mathrm{showing} \\ $$$${K}=\frac{\begin{vmatrix}{−\frac{\mathrm{1}}{\mathrm{2}}{E}_{{vv}} +{F}_{{uv}} −{G}_{{uu}} }&{\frac{\mathrm{1}}{\mathrm{2}}{E}_{{u}} }&{{F}_{{u}} −\frac{\mathrm{1}}{\mathrm{2}}{E}_{{v}} }\\{\:\:\:\:\:\:\:\:\:\:\:\:{F}_{{v}} −\frac{\mathrm{1}}{\mathrm{2}}{G}_{{u}} }&{\:\:\:{E}}&{\:\:\:\:\:\:{F}}\\{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}{G}_{{v}} }&{\:\:\:{F}}&{\:\:\:\:\:{G}}\end{vmatrix}−\begin{vmatrix}{\:\:\:\:\mathrm{0}}&{\frac{\mathrm{1}}{\mathrm{2}}{E}_{{v}} }&{\frac{\mathrm{1}}{\mathrm{2}}{G}_{{u}} }\\{\frac{\mathrm{1}}{\mathrm{2}}{E}_{{v}}…
Question Number 225604 by mr W last updated on 04/Nov/25 Commented by mr W last updated on 04/Nov/25 $${An}\:{uniform}\:{cylinder}\:{with}\:{radius}\:{R} \\ $$$${is}\:{spinned}\:{about}\:{its}\:{axis}\:{to}\:{the} \\ $$$${angular}\:{velocity}\:\omega_{\mathrm{0}} \:{and}\:{then}\:{placed} \\…
Question Number 225601 by gregori last updated on 04/Nov/25 $$\:\:\: \mathrm{2}^{\mathrm{2025}} ×\mathrm{3}^{\mathrm{2025}} \: \\ $$ Commented by mr W last updated on 04/Nov/25 $${the}\:{unit}\:{digit}\:{of}\:\mathrm{6}^{{n}} {is}\:{always}\:\mathrm{6}.…
Question Number 225581 by Lara2440 last updated on 03/Nov/25 $$\mathrm{prove} \\ $$$$\mathrm{Gauss}\:\mathrm{curvature}\:{K}\:\mathrm{intrinsic} \\ $$$$\mathrm{it}'\mathrm{s}\:\mathrm{the}\:\mathrm{same}\:\mathrm{thing}\:\mathrm{as}\:\mathrm{saying}; \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{Gauss}\:\mathrm{curvature}\:{K}\:\mathrm{can}\:\mathrm{only}\:\mathrm{consist}\:\mathrm{of} \\ $$$$\mathrm{First}\:\mathrm{Fundamental}\:\mathrm{Form}\:\mathrm{and}\:\mathrm{it}'\mathrm{s}\:\mathrm{Derivatives}. \\ $$ Terms of Service Privacy Policy…
Question Number 225568 by necx122 last updated on 03/Nov/25 $${A}\:{farmer}\:{produces}\:{seeds}\:{in}\:{packets} \\ $$$${for}\:{sale}.\:{The}\:{probability}\:{that}\:{a}\:{seed} \\ $$$${selected}\:{at}\:{random}\:{will}\:{grow}\:{is}\:\mathrm{0}.\mathrm{8}. \\ $$$${If}\:{there}\:{are}\:\mathrm{20}\:{seeds},\:{what}\:{is}\:{the} \\ $$$${probability}\:{that}\:{less}\:{than}\:\mathrm{2}\:{will}\:{not} \\ $$$${grow}? \\ $$ Commented by necx122…
Question Number 225563 by mr W last updated on 03/Nov/25 Commented by mr W last updated on 03/Nov/25 Commented by fantastic last updated on 03/Nov/25…
Question Number 225503 by Jyrgen last updated on 31/Oct/25 $${find}\:{x}\in\mathbb{C}\:{for}\:{r}\in\mathbb{R}\backslash\left\{\mathrm{0}\right\} \\ $$$$\left(−{r}\right)^{{x}} ={r} \\ $$ Answered by MrAjder last updated on 02/Nov/25 $$\left(−{r}\right)^{{x}} ={r} \\…
Question Number 225497 by gregori last updated on 31/Oct/25 Answered by Simurdiera last updated on 01/Nov/25 $$\begin{array}{|c|}{\mathrm{11}}\\\hline\end{array}\begin{cases}{{x}\:+\:{y}\:+\:\sqrt{{xy}}\:=\:\mathrm{28}\:\:\:\:\:\ldots\left(\mathrm{I}\right)}\\{{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{xy}\:=\:\mathrm{336}\:\:\:\:\:\ldots\left(\mathrm{II}\right)}\end{cases} \\ $$$$\mathrm{En}\:\left(\mathrm{II}\right),\:\mathrm{sumando}\:\mathrm{ceros} \\ $$$${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{xy}\:+\:{xy}\:−\:{xy}\:=\:\mathrm{336}…
Question Number 225506 by fantastic last updated on 31/Oct/25 Commented by fantastic last updated on 31/Oct/25 $${youre}\:{right}\:{sir} \\ $$ Commented by MirHasibulHossain last updated on…
Question Number 225490 by mr W last updated on 30/Oct/25 Commented by mr W last updated on 31/Oct/25 $${a}\:{funny}\:{clock}\:{created}\:{with}\:{Grapher} \\ $$ Commented by mr W…